Turbulent Boundary Layer under Simultaneous Effect of the Longitudinal Pressure Gradient, Injection (Suction), and Transverse Surface Curvature

The procedure successfully used in the construction of an algebraic model of turbulence for flows with an adverse pressure gradient [1] is used for the construction of a more general model of turbulence allowing for both the direct and cross effect of the factors acting simultaneously, namely, the longitudinal pressure drop, injection (suction) of a gas through a porous surface, and the transverse surface curvature. In contrast to the model proposed in [2] and based on the use of the Bradshow–Ferriss–Atwell equation for the turbulent stresses in determining the velocity scale in the outer region, the model suggested by us is fully based on the equation for the first moments written in terms of the law of the wall. The latter fact makes it possible to use only two empirical constants, as in [1], and to eliminate the stage of "tuning" the model, as in [2], which is associated with the fitting of three additional empirical constants characterizing the diffusion of shear stress under the effect of three external factors, namely, the pressure drop, injection (suction), and transverse curvature. In so doing, the testing results indicate that the proposed model proves to be quite competitive both with the model of [2] and with the most representative differential models of turbulence.